I have finally got Outlook 2010 on Windows 7 Home Premium to connect to Exchange 2013 installed on a Server 2012 R2 DC a DC that is connected to the local LAN, I have done this by manually setting up the connect via http proxy settings as follows:-.
URL to Exchange Proxy Server, I had to set to .co.uk">username@<external_domainname>.co.uk
**Why can I not connect in the same way as I connect to Exchange Server 2010 with just local NTLM Authentication and no proxy settings?.